2-连通图的单圈子图

Unicyclic subgraphs in 2-connected graphs

证明了如下结果:(1)一个2-连通图G的Θ-图是2(ρ-1)连通的;(2)如果一个2-连通图G有两个单圈支撑子图,且这两个单圈支撑子图分别含m和n个悬挂点(m<n),则图G至少有2(ρ-1)个含k个悬挂点的单圈支撑子图,这里m≤k≤n,ρ=|E(G)|-|V(G)|+1.

This paper proved the following results： （1） The Θ-graph of a 2-connected graph is 2 （ρ-1）connected; （2） if a 2-connected graph G has two unicyclic spanning subgraphs and the number of one-valent vertices of these two subgraphs are respectively rn and n（m〈n）, then for any integer k：m≤k≤n, there exist at least 2（ρ- 1）unicyclic subgraphs of graph G which have k one-valent vertices. Here, ρ is the dimension of the cycle space of G.